## Info

Pressure or speed

### Pressure or speed

Fig. 9.1 Power output and thermal efficiency of Stirling engines as a function of engine speed or pressure level. F fleets of dead volume, harmonic motion, and adiahatic compression and expansion on the ideal cycle the ideal Stirling engine there must he some void volume in the regenerator and other heat exchangers. Including this dead volume reduces the amplitude of the pressure excursion when the working fluid is moved from the cold to the hot space and results in a reduction in the power output per unit mass of working fluid, represented by the line 'B-B' in Fig. 9.1(a). The efficiency remains at the ideal cycle value.

A departure from discontinuous piston motion to the sinusoidal piston motion of the Schmidt isothermal cycle causes a redistribution of the working fluid between the compression, expansion and the dead space with consequent further reduction in the range of the pressure amplitude and power output. This is represented by the line 4C-C in big. 9.1(a). As before, the efficiency remains at the ideal cycle value.

In most of the mechanisms used to effect the volume variations the motion is not exactly sinusoidal. As an example, consider the simple crank slider mechanism shown in Fig. 9.2. The motion of the piston P may be represented by the equation:

(x/r) = (1 -cos 9) + (//r)( 1 -cos <*>) (9.1)

where x is the distance moved by the piston from the outer dead point A. r is the crank radius ! is the length of the connecting rod 0 is the crank angle </> is the connecting rod angle. The second term of the equation is the distortion to true sinusoidal motion of the first term imposed by the crank connecting rod obliquity,

Fig. 9.2. Simple crunk-slider mechanism.

The effect can be minimized by the use of a long connecting rod. but this cannol be taken too far as it leads to long, heavy machines.

The effect of non-sinusoidal piston motion is to further modify the mass distribution of working fluid in the engine and may or may not cause a reduction in the power output depending on the other engine parameters. In many cases the effect of non-sinusoidal piston motion is of secondary importance and often may be neglected, at least at the preliminary design stage.